KolmogorovDist

0th

Percentile

Generic function for the computation of the Kolmogorov distance of two distributions

Generic function for the computation of the Kolmogorov distance $d_\kappa$ of two distributions $P$ and $Q$ where the distributions are defined on a finite-dimensional Euclidean space $(\R^m,{\cal B}^m)$ with ${\cal B}^m$ the Borel-$\sigma$-algebra on $R^m$. The Kolmogorov distance is defined as $$d_\kappa(P,Q)=\sup{|P({y\in\R^m\,|\,y\le x})-Q({y\in\R^m\,|\,y\le x})| | x\in\R^m}$$ where $\le$ is coordinatewise on $\R^m$.

Keywords
distribution
Usage
KolmogorovDist(e1, e2, ...)
## S3 method for class 'AbscontDistribution,AbscontDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'AbscontDistribution,DiscreteDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'DiscreteDistribution,AbscontDistribution':
KolmogorovDist(e1,e2)
## S3 method for class 'DiscreteDistribution,DiscreteDistribution':
KolmogorovDist(e1,e2)
Arguments
e1
object of class "Distribution"
e2
object of class "Distribution"
...
further arguments to be used in particular methods (not in package distrEx)
Value

  • A list containing the following components:
  • e1object of class "Distribution"; distribution 1
  • e2object of class "Distribution"; distribution 2
  • Kolmogorov.distanceKolmogorov distance of e1 and e2

concept

distance

References

Huber, P.J. (1981) Robust Statistics. New York: Wiley. Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

See Also

ContaminationSize, TotalVarDist, HellingerDist, Distribution-class

Aliases
  • KolmogorovDist
  • KolmogorovDist-methods
  • KolmogorovDist,AbscontDistribution,AbscontDistribution-method
  • KolmogorovDist,AbscontDistribution,DiscreteDistribution-method
  • KolmogorovDist,DiscreteDistribution,DiscreteDistribution-method
  • KolmogorovDist,DiscreteDistribution,AbscontDistribution-method
Examples
KolmogorovDist(Norm(), Gumbel())
KolmogorovDist(Norm(), Td(10))
KolmogorovDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100))
KolmogorovDist(Pois(10), Binom(size = 20))
Documentation reproduced from package distrEx, version 1.9, License: GPL (version 2 or later)

Community examples

Looks like there are no examples yet.